Anna is counting the number of seeds in her fruit. Her watermelon has one less than three times the number of seeds as her apple. Her orange has 13 less than 5 times the number of seeds as her apple. Her watermelon has more seeds than her orange. Which inequality represents the number of seeds her apple could have?

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MrRoyal MrRoyal · Answer 1 · 2021-10-29T10:41:10+02:00

Inequalities are used to represent unequal expressions

The inequality that represents the number of seeds her apple could have is [tex]\mathbf{A < 6}[/tex]

Represent the fruits with the first letter.

So, we have:

[tex]\mathbf{W =3A - 1}[/tex] --- watermelon is one less than three times apple

[tex]\mathbf{O =5A - 13}[/tex] --- orange is thirteen less than five times apple

[tex]\mathbf{W > O}[/tex] --- the seeds in watermelon exceeds orange

Substitute expressions for W and O in [tex]\mathbf{W > O}[/tex]

[tex]\mathbf{3A - 1 > 5A - 13}[/tex]

Collect like terms

[tex]\mathbf{13- 1 > 5A - 3A}[/tex]

[tex]\mathbf{12 > 2A}[/tex]

Divide both sides by 2

[tex]\mathbf{6 > A}[/tex]

Rewrite as:

[tex]\mathbf{A < 6}[/tex]

The inequality that represents the number of seeds her apple could have is [tex]\mathbf{A < 6}[/tex]